Introduction to Options





Kerry Back

  • A financial option is a right to buy or sell a financial security.

  • The right trades separately from the (underlying) security and usually even on a different exchange.

  • The rights are not (usually) issued by the companies who issue the underlying securities.

    • Instead, the rights are created when someone buys one from someone else.
    • Open interest is the number that exist at any time.

  • A call option is the right to buy an asset at a pre-specified price.

  • A put option is the right to sell an asset at a pre-specified price.

  • The pre-specified price is called the exercise price or strike price.

  • An option is valid for a specified period of time, after which it expires.
    • Most financial options can be exercised at any time the owner wishes, prior to expiration. Such options are called American.
    • There are some options that can only be exercised on the expiration date. They are called European. Both types are traded on both continents.

  • If you’ve bought an option, you are “long.”” If you’ve sold an option, you are “short.”
  • After a trade occurs, the option clearinghouse steps in the middle and becomes the counterparty to both sides.
    • The long party has an option to buy from or sell to the clearinghouse at the strike.
    • The short party has an obligation to sell to or buy from the clearinghouse at the strike.

  • Usually buyers sell to close their position rather than exercising.
  • And sellers buy to close their positions rather than being obliged to buy/sell.
  • Open interest rises when a contract first begins to trade, then eventually declines as people trade to close their positions.

Open Interest Example

  • When a contract is first opened for trading, open interest is zero.
  • Suppose Andy buys a contract from Chloe, and Brooke buys a contract from David.
    • Longs = Andy and Brooke
    • Shorts = Chloe and David
    • Open interest = 2

  • Suppose Andy then sells a contract to David.
    • Andy: long + short = no position
    • David: short + long = no position
    • Longs = Brooke
    • Shorts = Chloe
    • Open interest = 1

Hedging, speculation, and income

  • You pay upfront to acquire an option.
    • The amount you pay is called the option premium.
    • It is not part of the contract but instead is determined in the market (like a stock price).
  • You buy options to hedge or to speculate. You sell options for income.
  • Sellers of options need to have sufficient equity in their accounts (margin). A buyer needs enough cash to pay the premium but no more (like buying a stock).

Moneyness

  • Borrowing language from horse racing, we say a call is

    • in the money if the underlying price is above the strike,
    • at the money if the underlying price equals the strike
    • out of the money if the underlying price is below the strike
  • The reverse for puts

  • Also, “deep in the money” and “deep out of the money”

Value of a call at maturity

  • At maturity (the expiration date), the value of a call is

\[\begin{cases} 0 & \text{if underlying < strike}\\ \text{underlying} - \text{strike} & \text{if underlying > strike} \end{cases} \]

  • Equivalently, the value of a call is

\[\max(\text{underlying price}-\text{strike}, 0)\]

With strike = 50,

Value of a put at maturity

  • At maturity, the value of a put is

\[\begin{cases} \text{strike} - \text{underlying} & \text{if underlying < strike}\\ 0 & \text{if underlying > strike} \end{cases} \]

  • Equivalently, the value of a put is

\[\max(\text{strike}-\text{underlying price}, 0)\]

With strike = 50,